Research

Mathematics and Statistics research strengths

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At its most fundamental level, mathematics is the study of quantity, number, shape, pattern and order. Some UQ researchers concentrate on pure mathematics research aimed at adding to humanity’s stock of knowledge at this fundamental level. Other researchers combine their knowledge of mathematics and statistics with modelling and the latest computer technology to solve problems in the physical, biological, medical and social sciences, and in engineering, information technology, economics and business.

UQ prides itself on both the depth and breadth of our research in Mathematics and Statistics, with significant contributions in a range of areas of Pure Mathematics, Applied Mathematics and Statistics. UQ was one of only three Australian universities to be ranked in all five specialised fields of Mathematics in the 2012 Excellence in Research for Australia exercise, and obtained the two highest ratings – above world standard and well above world standard – in more fields than any other university.

Mathematics and Statistics at UQ boasts numerous holders of prestigious Australian Research Council (ARC) Fellowships, including Laureate Fellowships, Australian Professorial Fellowships, Discovery Outstanding Researcher Awards, QEII Fellowships, and Australian Postdoctoral Fellowships, and Fellows of the Australian Academy of Science. Our staff have received further recognition in the form of prestigious international medals or awards, including the Australian Mathematical Society Medal.

UQ researchers have a wide network of partners including not only leading Australian and international universities, but also hospitals, research laboratories, State and Federal Government and industry partners.

The majority of UQ’s research in mathematics and statistics is concentrated in the School of Mathematics and Physics. There are also significant contributions from elsewhere in the Faculty of Science, as well as from:

  • Faculty of Business, Economics and Law
  • Australian Institute for Bioengineering and Nanotechnology
  • Institute for Social Science Research
  • Queensland Brain Institute
  • Sustainable Minerals Institute 

Mathematics and Statistics in brief

  • More than 40 full-time equivalent researchers
  • More than 50 PhD and MPhil students in 2014
  • More than 440 publications since 2008
  • More than $17.5 million in research funding since 2008
  • UQ Statistics and Numerical and Computational Mathematics research rated at the highest level – well above world standard – in the 2012 Excellence in Research for Australia exercise (the only institution to achieve this). Pure Mathematics and Applied Mathematics research rated above world standard.

Highlights of UQ Mathematics and Statistics

Pure mathematics 

Pure mathematicians at UQ study fundamental, theoretical questions and explore new, emerging areas of mathematics: 

  • The combinatorics group studies mathematically optimal configurations of objects, such as in networks, with strategic applications in digital signal reconstruction and transport logistics
  • In geometric and non-linear analysis, researchers study the equations that govern heat and fluid flow, as well as the evolution of abstract geometric surfaces
  • Research in algebra pursues answers to deep questions about numbers and the structure of algebraic objects that have eluded humanity for centuries
  • Research in computational topology seeks to develop cutting-edge software to solve geometric problems 

Our pure mathematicians also have industry and government partnerships demonstrating a range of applications for their results and techniques. For example, in a joint venture with Jeppesen Rail Logistics and Terminals, UQ researchers are developing virtual transport networks for reliability testing of commercial transportation software. In another project, sophisticated models for granular flow were developed in a partnership between UQ pure mathematicians, earth scientists and mining experts. 

Applied mathematics

UQ has leading expertise in a number of fields of bio-mathematics ranging from cellular biology to ecology. Some strengths in applied mathematics include:

  • Mathematical analysis of ecological and conservation biology problems and the provision of optimal management strategies
  • Modelling of biological process at a cellular level, including self-renewal of epithelial tissues, collective cell migration, and nervous system development and function
  • Collaborative projects with scientists and engineers, such as the optimal design and prototyping of titanium scaffolds for bone implants 

Much of this work involves collaboration with academic and industrial engineers, ecologists, biologists and medical researchers. For example, software developed at UQ for optimal marine reserve system design was used to rezone the Great Barrier Reef.

UQ also has a leading group in Mathematical Physics, which studies algebraic structures, their representation theory, and applications to exactly-solvable models of classical statistical mechanics, conformal and quantum field theory, and integrability of quantum many-body systems.  

Statistics

Statistics research at UQ is at the international forefront.

  • Multivariate statistics is used to develop cutting-edge statistical methodology and machine learning algorithms for the analysis of high-dimensional data, including image, genetic and genomic data. Advanced Monte Carlo methods such as the cross-entropy method are investigated to solve complicated optimisation and estimation problems in science, engineering and finance, such as the design of optimal electricity networks. Applied probability is used to describe and analyse random processes occurring in telecommunication networks, production scheduling, and ecology, such as finding optimal strategies for the control of invasive species.

  • UQ is also involved in groundbreaking research in applied statistics to assess spatial and temporal data occurring in nature and in society. For example, in partnership with the State Government and CSIRO, new insights have been gained into natural phenomena such as fluctuations in fish stock and water quality in Queensland. Another example is the development of novel statistical models capturing the interrelated nature of social processes, aimed at improving our understanding of pathways into and out of social and economic disadvantage for Australian families. These models are being developed using emerging longitudinal social survey and administrative data collected by State and Commonwealth Governments.